Question

ABCDE is a regular pentagon. In the given figure, all the circles have the centres at the vertices and all are of equal radius r. The sum of the area of all the shaded sections is

Answer 1

WShats the question?

Answer 2

WShats the question?

Answer 3

Ahh.. this one is a little tricky

Answer 4

You will have to calculate the area of the sector

Answer 5

See area of sector = \(\large{\cfrac{\text{central angle}}{360} \times {\text{area of circle}}}\)

Answer 6

area of the circle =pie r^2

Answer 7

Very good.

Answer 8

Now what is the angle the shaded part makes at centre ?

Answer 9

area of the sector=pie r^2 theta/360 right.u r formula is not visible .

Answer 10

No problem. Your formula is perfect

Answer 11

1/4pie .r^2

Answer 12

No no no theta is NOT 90 here

Answer 13

pie.(r^2/4)

Answer 14

How did you get that 4 ?

Answer 15

sorry .the internal angle of pentagon is 108degree

Answer 16

Very good

Answer 17

So theta = 108 degrees

Answer 18

Now calculate the area of the sector

Answer 19

pie.r^2.108/360

Answer 20

Fantastic...

Answer 21

Now required area = number of sectors * area of each sector

Answer 22

5*33r^2/35

Answer 23

How did you get 33/35 ?

Answer 24

pie.r^2.108/360=33/35r^2.

Answer 25

5*pie.r^2.108/360

Answer 26

540/360.pie.r^2

Answer 27

Ohh good

Answer 28

Yes correct :)

Answer 29

Great work.. See, you were very close to the answer this time :)

Answer 30

you are a fast learner

Answer 31

yes.i always struggle a lot for small things

Answer 32

Its okay.. many do